Question : S, T, and U can complete a work in 40, 48, and 60 days, respectively. They received Rs. 10,800 to complete the work. They began the work together, but T left 2 days before the completion of the work and U left 5 days before the completion of the work. S has completed the remaining work alone. What is the share of S (in Rs.) from the total money?
Option 1: 4000
Option 2: 4320
Option 3: 4500
Option 4: 4860
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Correct Answer: 4860
Solution :
S’s 1 day work =$\frac{1}{40}$
T’s 1 day work = $\frac{1}{48}$
U’s 1 day work = $\frac{1}{60}$
Let the work be completed in $x$ days, such that S worked for all $x$ days, T worked for $(x - 2)$ days, and U for $(x - 5)$ days.
⇒ $\frac{x}{40}+ \frac{x-2}{48} + \frac{x-5}{60}= 1$
⇒ $6x + 5(x - 2) + 4(x - 5) = 240$
⇒ $6x + 5x - 10 + 4x - 20 = 240$
⇒ $15x = 270$
⇒ $x = \frac{270}{15}=18$ days
Hence, ratio of their share =$\frac{18}{40} ∶ \frac{16}{48} ∶ \frac{13}{60} = 27∶20∶13$
Sum of ratios = 27 + 20 + 13 = 60
$\therefore$ S’s share = $\frac{27}{60}× 10800 = 4860$
Hence, the correct answer is 4860.
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